Modern Physics Letters A

A viable formulation of gauge theory with extra generations in terms of quaternionic fields is presented. For the theory to be acceptable, the number of generations should be ≥ 4. The quark–lepton mass matrices are generalized into quaternionic matrices. It is concluded that explicit CP-violation automatically disappears in both strong- and weak-interaction sectors.

The B_s→ϕψ decay is modeled through the inclusive b→ sψ decay. Using the vector meson dominance model, the amplitude for the chain process B_s→ϕ;ψ→ϕγ→γγ is estimated and it is found to be at most 4% of the corresponding amplitude from the O₇ type LD contribution. The intermediate amplitude for the process B_s→ϕγ is compared with the corresponding one obtained by a different approach based on the interaction of the virtual charm quark loop with soft gluons.⁷ Both amplitudes are found to agree within 10%. Further the influence on the branching ratio B(B_s→γγ)_SD+LDO7 from inclusive b→ sψ is estimated to be less than 1%.

We show how the periods can be evaluated in Seiberg–Witten theories and in K3-fibered Calabi–Yau manifolds by using fibrations of the theories. In the Seiberg–Witten theories, it is shown that the dual pair of fields can be constructed from the classical fields in a simple form.

As for Calabi–Yau manifolds which are fibrations of K3 surface, we obtain the solutions of the Picard–Fuchs equations from the periods of K3 surface. By utilizing the expression of periods for two-parameter models of type-II string, we derive the solutions of the Picard–Fuchs equations around the points of enhanced gauge symmetry and show a simple connection to the SU(2) Seiberg–Witten theory.

The properties of relativistic particles in the quasiclassical region are investigated. The relativistic semiclassical wave equation appropriate in the quasiclassical region is derived. It is shown that the leading-order WKB quantization rule is the appropriate method to solve the equation obtained.

In our letter we deal with the inclusive and exclusive decay of B^- meson. The inclusive b→dγ decay has been considered here including the QCD corrections to the Wilson coefficients and the matrix elements of the operators in the effective Hamiltonian. We calculate the O(α_s) virtual corrections to the matrix element for b→dγ, taking into account the contributions of the four-fermion operator O₂ and the electromagnetic and color dipole type operators. It drastically reduces the large scale dependence of the leading logarithmic approximation. Moreover, while we are considering the exclusive B^-→ρ^-γ decay, we have taken into consideration both the short distance as well as long distance contributions. Therefore, we have obtained better result for the partial decay width of B^-→ρ^-γ.

A modified BCS approach is used to interpret the first excited state of ¹¹Li halo nuclei. In this scheme, a simple two-level model calculation is performed leading to results in good agreement with the experimental results for ¹¹Li for both ground and first excited states. A comparison with exact and QRPA calculations is also presented.

The Schwinger–De Witt expansion for the evolution operator kernel of the Schrödinger equation is studied for convergence. It is established that divergence of this expansion which is usually implied for all continuous potentials, excluding those of the form V(q)=aq²+bq+c, takes place only if the coupling constant g is treated as an independent variable. But the expansion may be convergent for some kinds of potentials and for some discrete values of charge, if the latter is considered as fixed parameter. Class of such potentials is interesting because inside it the property of discreteness of the charge in nature is reproduced in theory in the natural way.

Dimensional reduction in quantum field theory is discussed with emphasis on the difference between "geometric" versus "kinematic" dimensional reduction. It is shown how environmentally friendly renormalization can also be applied to the latter case. As concrete examples, finite temperature λϕ⁴ theory and the Regge limit of ϕ²ψ are considered. In the latter, crossover between large and small energies at fixed momentum transfer is considered and asymptotic forms of the crossover scaling functions are exhibited for all two-particle scattering processes in this channel.

A nonhomogeneous universe with vacuum energy, but without space–time expansion, is utilized together with gravitational and Doppler redshifts as the basis for proposing a new interpretation of the Hubble relation and the 2.7 K Cosmic Blackbody Radiation.